Probabilistic Forecasting of Customer Purchase Activity

Probabilistic Forecasting of Customer Purchase Activity


In non-contractual business settings, anticipation of customer visitation and churn activity relies strongly on structured data analytics. However, predicting individual behaviors is extremely difficult when only short transaction histories exist. For these cases, leading marketing researchers have designed probabilistic mathematical models which utilize patterns from customer cohort groupings. Once this type of model has been fitted to a cohort, likelihood predictions can be made regarding churn propensity and future visitation frequency, even for individuals having relatively short purchase histories. Unfortunately, models of this form have not yet been widely implemented in commercial statistical software packages.



In order to expand our data processing capability for Customer-Base Analysis, AlgoTactica has designed object-oriented MATLAB implementations of three of the best-known probabilistic cohort analysis models. To investigate predictive capability, these designs were fitted to a retail data set in which 91% of the customers had less than 6 repeat purchases beyond their first transaction with the vendor. The results shown here are for a model in which purchase rates follow a Negative Binomial distribution, and customer churn rates follow a Pareto.



In the Model Validation: Repeat Purchases graph, the blue line compares the known relationships between the training period (x-axis) and the validation test period (y-axis). For example, the blue line shows that customers who averaged 3 or 6 visits (x-axis) in the training period averaged 0.7 or 2.0 (y-axis) visits in the validation period. The red line shows the result after out-of-sample forecasted revisit numbers are produced for each customer by the model and then averaged. For customers known to average 3 or 6 visits during training, the model predicts that they will average 0.8 or 1.8 in the validation period, agreeing well with the known values of 0.7 or 2.0. Overall, the red curve shows that the predicted repeat visit rates agree closely with the known rates.

The Expected Transactions Next 30 Days and Future Purchase Probability contour plots display model predictions pertaining to future customer behavior, and are based on behaviors measured during the 71-week history of the cohort. The x-axis represents total cumulative transactions to date for any given customer, and the y-axis represents the number of weeks since their last transaction. From the Expected Transactions plot it is seen that a customer whose total transactions to date is greater than 100, and who has purchased within the past week, can be expected to make approximately 4 purchases during the next month. However, customers who have made fewer than 20 purchases overall, and who have not bought within the last several weeks, can only be expected to make a maximum of 1 purchase.

The Future Purchase Probability contour plot anticipates the likelihood that a customer will return, and reveals how the model accommodates past behaviors. For instance, customers who have had 100 transactions and a recency of 1-2 weeks, have the same probability as those who have had a much lower total of 10 transactions and a recency of 10 weeks. Here the model accounts for the fact that the low count customers visit only occasionally, so that a longer period between transactions is not necessarily an indicator that they have dropped out. However, if a 100-transaction customer were to score a recency of 10 weeks, then it is highly likely that they have churned.

The Purchase Probability graphs for Customers 855 and 838 show how the model can also make inferences about individual customers. The red line indicates the probability that the customer is still active, while the vertical grey lines denote the dates on which there has bee a transaction during the past 71 weeks. Customer 838 has not purchased within the past 25 weeks, so the model estimates that there is a low probability of still being active. Based on this observation, 838 could now be offered special marketing incentives to encourage returning as a customer to the business.

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